Somebody is going to wring some cost savings out of the structure of Mondelez (MDLZ) - Get Report at some point. The question is whether it is going to be the existing management, or the operating performance fiends at Kraft Heinz (KHC) - Get Report .

Shares of Mondelez jumped 4% in Tuesday's trading, as the rumor mills revived the reports that the Oreo maker was back on the auction block. The stock traded at $46, back in range of its mid-summer highs.

The precipitant for the latest round of speculation: reports that 3G, the Brazilian asset manager, has set about to raise a new $8 billion to $10 billion fund, an initiative that would presumably be used to finance 3G's next investment - or likely co-investment - perhaps in another U.S. food maker. 3G, which has partnered with Berkshire Hathaway (BRK.A) - Get Report in the past on acquisitions, would presumably use the two enterprises' joint venture Kraft Heinz as the takeover vehicle in any Mondelez play.

"The fit seems natural," Brittany Weissman, a food industry analyst at Edward Jones, said in an interview Tuesday.

Kraft would like to expand its presence on the international stage, and Mondelez still has a portfolio of global brands formerly owned by Kraft. Kraft and Mondelez, of course, split into two companies in 2011: the larger global business, which includes, in addition to Oreo, brands such as Cadbury and Wheat Thins, became Mondelez; while cheese products, coffee, Jell-O and Planters nuts were retained by the the Kraft Foods Group. Kraft then merged with Heinz in 2015 under the direction of the 3G/Berkshire initiative.

Mondelez would look attractive to a buyer such as 3G because its operating costs are higher than the industry average, suggesting there are ripe opportunities for a buyer to squeeze some of those costs out of the business. "As you look at the food group to determine the companies with the biggest gap in profit margins, the operator that falls to the bottom would be a Mondelez or a Kellogg," Weissman said.

"A 3G angle would be interesting," Gaurav Gupta, principal at global consulting firm Kotter International, said in an interview Tuesday. "3G would have to come in with a plan for aggressive cost cutting, and believe firmly they can achieve it."

Mondelez has launched its own cost cutting program, stating its ambition to raise profit margins to 17% or 18% from the current level of 15%. It's an initiative that has met with the approval of some of the influential activists who have taken positions in Mondelez. Most notably, Bill Ackman at Pershing Square has backed away from his previous stance of urging Mondelez to combine with the Frito-Lay operation at Pepsico (PEP) - Get Report  to maintain its focus on the cost cutting program.

The early returns on cost cutting initiatives - improving automation, moving factories closer to raw material sites, and other efforts - are relatively easy to realize, Gupta said. It's the second round of margin improvements - where real profit growth is realized - that can be thornier.

The launch of the cost cutting initiative was one of the reasons that some skeptics questioned why Mondelez made its high-profile, but ultimately unsuccessful, bid for Hershey  (HSY) - Get Report this year. But at the time it was thought that buying Hershey would swell the Mondelez market value enough to effectively insulate the company against a takeover.

Gupta said he doubted if Mondelez was focusing on finding another takeover target to swallow in order to thwart any unwanted overtures from an outside company. "From my perspective, I'm not expecting a big announcement from Mondelez" about pursuing additional targets.

Weissman said that she remained positive about Mondelez as a standalone company, though she acknowledged that the takeover prospect added an intriguing dimension to the fundamental story. 3G isn't considered to be averse to lobbing in some attractive premiums for assets that it wants, as long as it can see, though cost cuts, a way to make the takeover attractive.

Clearly, 3G is early in the fund raising effort, so it could take some time for any bid for Mondelez - assuming it comes to fruition - to arrive. But investors don't seem inclined to wait for the numbers to attach to a takeover offer to pile into the stock of the grocery products maker

No disclosures.